$K$ is the midpoint of $\overline{JL}$ $J$ $K$ $L$ If: $ JK = 8x - 9$ and $ KL = 2x + 27$ Find $JL$.
Answer: A midpoint divides a segment into two segments with equal lengths. ${JK} = {KL}$ Substitute in the expressions that were given for each length: $ {8x - 9} = {2x + 27}$ Solve for $x$ $ 6x = 36$ $ x = 6$ Substitute $6$ for $x$ in the expressions that were given for $JK$ and $KL$ $ JK = 8({6}) - 9$ $ KL = 2({6}) + 27$ $ JK = 48 - 9$ $ KL = 12 + 27$ $ JK = 39$ $ KL = 39$ To find the length $JL$ , add the lengths ${JK}$ and ${KL}$ $ JL = {JK} + {KL}$ $ JL = {39} + {39}$ $ JL = 78$